Etymology
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languid (adj.)

1590s, from French languide (16c.) and directly from Latin languidus "faint, listless, and sluggish from weakness, fatigue, or want of energy," from languere "be weak, be fatigued, be faint, be listless," from PIE *langu-, from root *sleg- "be slack, be languid." Related: Languidly; languidness.

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*sleg- 
*slēg-, also *lēg-, Proto-Indo-European root meaning "be slack, be languid."

It forms all or part of: algolagnia; catalectic; laches; languid; languish; lax; lease; lessor; lush; relax; release; relish; slack (adj.); sleep.

It is the hypothetical source of/evidence for its existence is provided by: Greek legein "to leave off, stop," lagnein "to lust;" Latin languere "to be faint, weary," laxus "wide, spacious, roomy;" Old Church Slavonic slabu "lax, weak;" Lithuanian silpnas "weak."
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listless (adj.)
"languid and unresponsive, slothful," mid-15c., from Middle English liste "pleasure, joy, delight" (see list (v.4)) + -less. Spenser, if no one else, tried listful (1590s). Related: Listlessly; listlessness.
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debilitate (v.)

"weaken, impair the strength of, enfeeble, make inactive or languid," 1530s, from Latin debilitatus, past participle of debilitare "to weaken," from debilis "weak, helpless," from de "from, away" (see de-) + -bilis "strength," from PIE root *bel- "strong" (see Bolshevik). Related: Debilitated; debilitating.

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relax (v.)

late 14c., relaxen, "to make (something) less compact or dense" (transitive), originally especially in medicine, of muscles, etc., from Old French relaschier "set free; soften; reduce" (14c.) and directly from Latin relaxare "relax, loosen, open, stretch out, widen again; make loose," from re- "back" (see re-) + laxare "loosen," from laxus "loose" (from PIE root *sleg- "be slack, be languid"). A doublet of release.

Meaning "decrease tension" is from early 15c. From 1660s as "to make less severe or rigorous." Intransitive sense of "become loose or languid" is by 1762; that of "become less tense" is recorded from 1935. Of persons, "to become less formal," by 1837. Related: Relaxed; relaxing. As a noun, "relaxation, an act of relaxing," from 17c.

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lessor (n.)
"one who grants a lease," late 14c., from Anglo-French lessor (late 13c.), from verb lesser "to let, to leave" (10c., Modern French laisser), from Latin laxare, from laxus "loose" (from PIE root *sleg- "be slack, be languid").
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algolagnia (n.)
"sado-masochism, sexuality that fetishizes violence and pain," 1900, Modern Latin, coined in German in 1892 by German doctor and paranormalist Albert von Schrenck-Notzing (1862-1929) from Greek algos "pain" (see -algia) + lagneia "lust," from lagnein "to lust," from PIE root *sleg- "be slack, be languid."
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reanimate (v.)

also re-animate, "restore to life, make alive again, revive, resuscitate," 1610s, in both spiritual and physical senses, from re- "back, again" + animate (v.) "endow with life." Sense of "revive when dull or languid" is by 1762. Related: Reanimated; reanimating.

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slack (adj.)

Old English slæc "remiss, lax, characterized by lack of energy, sluggish, indolent, languid; slow, gentle, easy," from Proto-Germanic *slakas (source also of Old Saxon slak, Old Norse slakr, Old High German slah "slack," Middle Dutch lac "fault, lack"), from PIE root *sleg- "be slack, be languid."

Sense of "not tight" (in reference to things) is first recorded c. 1300. As an adverb from late 14c. Slack-key (1975) translates Hawaiian ki ho'alu. Slack water (n.) "time when tide is not flowing" is from 1769. Slack-handed "remiss" is from 1670s. Slack-baked "baked imperfectly, half-baked" is from 1823; figuratively from 1840.

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drowsy (adj.)

"inclined to sleep, sleepy," 1520s, probably ultimately from Old English drusan, drusian "sink," also "become languid, slow, or inactive" (related to dreosan "to fall;" see dreary). There is no record of it in Middle English. Related: Drowsily; drowsiness.

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